What I did to reproduce the problem:
rails new play --css tailwind
cd play
rails generate scaffold say hello
bin/dev
Adding bg-green-600 to app/views/say/hello.html.erb worked at this point.
Stopping the server, running rails assets:precompile, restarting the server, and then changing the color to bg-sky-600 did not work - the background was white – this matched what you reported.
Stopping the server, running rails assets:clobber, and restarting the server, and I can see the new color. I can then change the color to bg-red-600 and see the results of my change.